1. Field of Invention
The present invention relates to circuitry for analyzing a dynamic system and more particularly to the application of this circuitry to a vibrating beam accelerometer ("VBA"). The circuitry analyzes a pair of frequencies which are related to natural frequency as a function of a force applied to a VBA to approximate ##EQU2##
2. Description of the Related Art
The term "system" is defined as an assemblage of objects united by some form of interaction or interdependence. For a dynamic system, there is the added restriction that the interaction or interdependence will vary with time. This dynamic behavior has been characterized by observing certain relationships, including the relationship between frequency and natural frequency: EQU W=W.sub.n (1+KT).sup.1/2 ( 1)
where W is a frequency, W.sub.n is a natural frequency, K is a constant, and T is a force, for example, the tension of a vibrating beam. The characterization of the variables are typical in the mechanical engineering arts. The equation has been applied to a wide range of dynamic systems, and a basic description of this phenomenon can be found in Norman H. Beachley and Howard L. Harrison, Introduction to Dynamic Systems (1978). As applied in a VBA, the difference in two frequencies is used to compute T, which is then used to calculate acceleration and velocity. For example, acceleration may be defined as being equal to the constant K times the difference in two frequencies (W.sub.1 -W.sub.2).
In designing circuitry to analyze the relationships in equation 1, a fundamental problem has been the non-linear nature of the equation. It has always been assumed that the effects of this non-linearity could be overcome by using a computer to make linear calculations and then to compensate for the error caused by the non-linearity. However, the presence of high levels of vibration produces a strong bias which normally makes computer compensation difficult and unreliable. This is true because the bias is determined by the harmonic content of the vibration and computer iteration is slow compared to higher vibration frequencies.
In practical applications such as a VBA, the presence of very high levels of vibration, severe acceleration and the non-linearity causes a large static error in the acceleration output. This acceleration error cannot be reduced by computer correction for cases where the vibration frequency is greater than one-half the computer sampling frequency. If the vibration level is separately observed and its wave-shape is known, correction is possible. However, this approach would appear to require the use of a plurality of additional accelerometers for sensing. Thus, the applications of such dynamic system analysis circuitry have been severely limited.